It is just a week into the Labour leadership contest and Andy Burnham, the frontrunner according to the bookies, admits that it already seems to have “lasted for ever”.

One fancied prospect, Dan Jarvis, has ruled himself out because of family commitments, while another, shadow business secretary Chuka Umunna, dramatically pulled out last Friday morning within three days of declaring his interest via a decidedly low-grade video clip from Swindon. Umunna said he was uncomfortable with the levels of scrutiny that had encompassed him and his family since he showed his hand.

In his first interview since launching his own leadership campaign, Burnham, 45, who stood in the 2010 contest only to come fourth out of the five candidates, is sympathetic to Umunna’s decision. But in the wake of a disastrous general election defeat, and with a huge rebuilding job to be done for Labour to stand any chance in the 2020 election, it seems now is not the time for platitudes.

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Umunna’s decision, Burnham says, highlights the need for Labour to have a more experienced leader, no matter the allure of a fresh face. “I think he has made the right decision and I think he has got a massive future in the Labour party – and I mean a massive future,” Burnham says.

Asked why the decision by Umunna, a Blairite favourite, to halt his bid, was the right one, he adds: “I think it was possibly too early to stand. It is a punishing experience. I have been through it once before, and it does test you on levels you have never been tested on before. You do have to be ready for that before you step over that line.

“Leadership is about experience and really having a rounded understanding that you are facing not just the Labour party but the country at every level. I was not ready to begin to do that after five years in parliament. I might have thought I was, but I wasn’t.”

With this swift dispatch of the hopes of two of his other more junior rivals completed – shadow health minister Liz Kendall and shadow education secretary Tristram Hunt were both elected only in 2010 – Burnham, twice a cabinet minister and first elected in 2001, moves on to deal with some further obstacles to his progress.

The Conservatives have been successful in peddling the line that Labour spending left the country unable to deal with the disaster. On that foundation, chancellor George Osborne has even built the claim that it was “Labour’s great recession” that gripped the world after the crash in the American sub-prime mortgage industry.

A decidedly uncomfortable moment during the BBC’s Question Time election special, between one angry man and Ed Miliband, who refused to admit any spending profligacy proved to be, in Burnham’s words, “a very big moment in the campaign”.

Last week, Yvette Cooper – a seasoned Labour hand who has had government experience both as work and pensions secretary and as chief secretary to the Treasury, and is perhaps Burnham’s greatest leadership rival – suggested she agreed with Miliband’s refusal to accept blame. She pointed out that “the budget deficit at the time was something like 0.6% – the current deficit”.

And neither is Burnham in the business of trashing Labour’s record. He believes that a reason for some of Labour’s difficulties over the past five years was the decision by Miliband to effectively disown the Blair and Brown years. “I think [the break] was too strong and, looking back, I would consider that to be a mistake,” he says.

He clearly wishes to rebuild Blair’s “big tent” idea, rejecting the mansion tax as symbolising “the politics of envy”, something the public doesn’t like. “My campaign is ‘heart of Labour’,” he says. “I am not saying we are about one side of the party. I was loyal to Tony Blair, loyal to Gordon Brown, loyal to Ed Miliband. I have never been into factional politics.”

He has signed up Blair’s one-time flatmate, Lord Falconer, as a supporter. But he recognises that public anger over the recession needs to be answered. He starts by noting that under Labour between 1997 and 2001 the UK “ran more surpluses … than they did in 18 years of Tory government”. He further defends the decision by Blair to then “rebuild the public realm”.

Burnham says he sympathises with Chuka Umunna’s decision to withdraw from the leadership race. ‘I think he has got a massive future in the Labour party – and I mean a massive future.’ Photograph: Ben Stansall/AFP/Getty Images

But, he says, his defence cannot be too fulsome. In those final years, he admits, too much was spent and the country subsequently did suffer because of it.

“I was the chief secretary to the Treasury who did the last spending review of the last Labour government [in 2007] and my instructions from [chancellor] Alistair Darling were to settle government departments at around 1%-1.5% – lower than overall growth in the economy,” he says.

“I remember colleagues saying: why are you being so tough? I think Gordon and Alistair said we had been at the limits of what had been prudent. Cameron and Osborne called that spending review tough.

“[But] to answer your question: we didn’t prioritise deficit reduction early enough. Having made that conscious decision to invest in the early part of the last decade, we should have been bringing that deficit by the middle part of that decade back to surplus. We didn’t, and the deficit carried on up to 2007. Therefore we weren’t in a strong enough position when the crash came.”

It is Burnham’s hope that this admission can form part of Labour’s comeback. It is one of three issues on which Burnham believes his party has struggled. “I see those issues as our economic credibility, our relationship with business – which is linked to that – and, thirdly, immigration.”

For him, the in/out referendum on Britain’s membership is the event that will allow him to present a new Labour stance. Privately, he says, he has disagreed for some time with Miliband’s line that an EU referendum should take place only if further powers are taken away from Britain through treaty change. “In the second half of the last parliament I thought we had to change our position. The country has clearly decided it wants to challenge and interrogate its relationship with Europe.”

So, he calls on Cameron to bring the referendum on Europe forward to 2016. Last week, the governor of the Bank of England, Mark Carney, said industry leaders were unhappy about the continuing uncertainty, and that is also a concern for Burnham, he says. He wants business generally to know that he is concerned. “I want the Alan Sugars of this world back in the Labour party – and him as well.”

But the shadow health secretary also warns the prime minister that he must also deliver a “tough but fair” package on immigration in his renegotiations before the referendum if he is to stand any chance of keeping the UK in the European Union.

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“What I am giving a very large warning about is that we risk losing if we have not made some significant changes to the way immigration works across the EU,” he says. “We need a package of changes so that there is no entitlement to benefits [for immigrants] for at least two years.

In general, he says, he doesn’t think that his own constituents object to migrant labour in itself. “Some might [disagree], but most accept that if people want to come to work they have no problem with that. My own dad left the north-west when I was young in the late 1980s-early 1990s because there was no work. Famously, that generation did that – Auf Wiedersehen, Pet and all that – and went to Germany and Ireland.

“How hypocritical would it be of me now to say that is wrong? If it was good enough for people here, then it is good enough for others. Freedom of movement is a two-way street. But freedom to work is not the same as freedom to claim. And I think that is where the commonsense view of most British people is.”

Burnham also believes the Tories need to address the tendency for some companies to import workers from the European Union and hire them through overseas-based agencies which pay below the minimum wage. These issues kept on coming up on the doorsteps during the ill-fated general election campaign, he says.

But can Burnham, the MP for Leigh in Greater Manchester, who says he already has the names of the required 35 MPs willing to nominate his candidacy, be the man to get Labour back in power in just five years’ time?

“Yes. I can do it if I set out right now and go straight to these issues that I have identified today. No beating about the bush. Get the right foundations down, get off on the right foot – and, beyond that, sell a bigger vision about what Labour is about.”

On his family‘I will continue to take my daughter to her netball and my son to his rugby league on a Sunday morning because that is just important – and makes you do a better job, to be honest. We are doing it as a family.’

On the 2010 decision to elect Ed Miliband as leader‘I voted for David, but I understand why the party chose Ed, because he more than anybody in the race showed that he had understood where we had gone wrong.’

On the Blair and Brown years‘I have conceded a point about spending, and rightly, but overall I will be resolutely defending the record of the 1997-2010 Labour government because it was a good record: it was a record we should be proud of, that party members should be proud of.’

On Miliband’s predators-versus-producers 2011 conference speech‘I think there were a few failures of communication in the last five years and this was one of them.’

On the mansion tax‘I have never been the trade unions’ man, if you like. They didn’t support me in the 2010 contest. I changed health policy away from the market because I believe that is what the public support, not because I was told by anybody.’

On the unions‘I think we have got to get away from things that look like symbolism. I am going to put the mansion tax in that category. I am not saying it was necessarily completely the wrong thing to do, but in its name I think it spoke to something that the public don’t particularly like, which is the politics of envy.’

The man who wrote his party’s manifesto, is under no illusions about the task facing Labour. He believes his duty lies in being brutally honest about what it got wrong and what has to be done to save the party from the existential threat that some senior figures still refuse to recognise